Install Alcove Bathtub with no front skirt

I've purchase the acryllic Azzurra Envy tub and am putting into 3 wall alcove. Tub has integrated tile flange on 3 sides and no front apron. I intend to tile the front of the tub area and need to ensure it is flush to the front lip of tub given limited space next to the bathtub. See the attached pics for how I'd like the tub to look.

My issue is that due to the narrow ledge, a typical 2X4 frame with 1/2 inch backerboard would create a significant ledge. I basically have 1.5 inches to work with (including tiles).

I'm considering either building a frame with 1X4 to support the front lip and then using 1/4 inch Hardiboard as the surface to tile on but am concerned the frame won't have the strength to deal any flex on the front ledge should someone sit on it (should be minimal given other 3 sides screwed into walls).

Other option I can see is using a single piece 1/2inch plywood which would be supported only on the bottom by a 2X4 and either side of the tub. I'd then use something to seal the plywood so that the tile takes to it. Would this be any stronger than the 1X4 frame option? This was the method suggested by the "help" people at Azzura but they also suggested I ask my contractor (I don't have one and will be doing the install myself).